Map-colouring questions ask for the fewest colours that keep neighbouring regions different. ASO 2021 asked one with concentric circles.
Rules
- Regions that only touch at a point may share a colour. Regions that share a line may not.
- A chessboard grid needs 2 colours.
- A ring of sectors needs 2 colours if the number of sectors is even and 3 if it is odd.
- A region that touches every region of a ring (like the centre circle) needs one extra colour.
- No flat map ever needs more than 4 colours.
Method
Start with the region that has the most neighbours. Colour it, then give its neighbours the smallest colours you can, and go outwards. If you are forced to use a new colour, check whether a different choice earlier would have avoided it.